Consider all possible permutations of the letters of the word ENDEANOEL.
Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the matrix given in the ORS.
Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the matrix given in the ORS.
| Column I | Column II |
|---|---|
| (A) The number of permutations containing the word ENDEA is | (p) 5! |
| (B) The number of permutations in which the letter E occurs in the first and the last positions is | (q) 2 ×5! |
| (C) The number of permutations in which none of the letters D, L, N occurs in the last five positions is | (r) 7 × 5! |
| (D) The number of permutations in which the letters A, E, O occur only in odd positions is | (s) 21×5! |
Answer: A → I, B → IV, C → II, D → II
Solution
The word ENDEANOEL has 9 letters: E(3), N(2), D(1), A(1), O(1), L(1). (A) Treat ENDEA as one block; arrange 5 units (ENDEA, N, O, E, L): 5! ways. (B) E at first and last; arrange middle 7 letters with E(1), N(2): . (C) First 4 positions from {E, E, E, A, O} (5 letters, 3 E's): ways; last 5 from {N, N, D, L, remaining}: ways; total . (D) Odd positions (5) for A, E, O (with E repeated): ways; even positions (4) for D, L, N, N: ways; total .
JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Match the columns